The UK health secretary said on Sunday that it was "appropriate" to push on with the major easing of lockdown in England on Monday despite warnings from scientists and medics.
But he warned the highly transmissible variant could "spread like wildfire among the unvaccinated groups" as he urged people to come forward for jabs when eligible.
Much of Scotland is also due to move to level two from Monday, but Glasgow and Moray will remain in level three due to a rise in Covid cases in both regions. In Glasgow, the higher number of cases was linked to the Indian variant by First Minister Nicola Sturgeon on Friday.
Mr Hancock was also forced to defend the UK Government against criticism it acted too late in imposing heightened border restrictions for travel from India.
The Cabinet minister said there were now more than 1,300 cases of the so-called Indian variant in total and it is becoming "the dominant strain" in areas including Bolton and Blackburn in the North West.
But offering good news to plans to ease restrictions without unleashing a fresh wave of infections and deaths, Mr Hancock said there is "new very early data" from Oxford University giving confidence that existing vaccines work against the variant.
"That means that we can stay on course with our strategy of using the vaccine to deal with the pandemic and opening up carefully and cautiously, but we do need to be really very vigilant to the spread of the disease," he told Sky s Sophy Ridge On Sunday.
"We have a high degree of confidence that the vaccine will overcome."
Mr Hancock said the government would decide on June 14 whether all legal restrictions could be ended in England in the final step of the road map out of lockdown on June 21.
He did not rule out the possibility that Monday's easing may have to be reversed if the strain turns out to be very highly transmissible, but said the hope is the "cautious and irreversible approach" can continue.
The Cabinet minister replied "we do not rule that out" when asked about the prospect of specific areas having heightened restrictions compared to tackle variants.
"The approach we're taking in Bolton and Blackburn is to absolutely pile in testing and vaccinations to try to get on top of this," he told Ridge.
"So at the moment we're taking the approach that worked in south London, which is this massive surge testing, but of course we don't rule out further action.
"Given though Bolton has been in some form of kind of a lockdown for a year, it's not a step we want to take but of course we might have to take it and we will if it's necessary to protect people."
Mr Hancock later told the BBC's Andrew Marr Show it was "quite likely" the Indian variant of Covid-19 would become the dominant variant in the UK.
He told: We don't know exactly how much more transmissible it is, but I think it is likely it will become the dominant variant here.”